Wyniki wyszukiwania - BazTech

1

Galerkin method for bending analysis of beams on non-homogeneous foundation

Musa A., E., S.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 3

61--72

EN

In this study, a mathematical formulation for static bending analysis of a beam on a non-homogenous foundation is presented. The proposed method offers an accurate procedure for analysis and design of a beam resting on a varying soil bed. The Winkler foundation model is used and presented using discontinuous functions to account for the sudden change in the soil stiffness coefficient. The solution of the governing differential equation is then obtained using the Galerkin method with the help of approximation functions that satisfy the boundary conditions. A systematic approach for setting the approximation functions for different support and soil conditions is suggested. The accuracy of the proposed method is verified through two numerical examples, and they showed an excellent agreement with the finite element method (FEM) and available literature results.

2

Recursive differentiation method: application to the analysis of beams on two parameter foundations

Hassan M. T., Doha E. H.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 1

15--26

EN

The recursive differentiation method (RDM) is introduced and employed to obtain analytical solutions for static and dynamic stability parameters of beams resting on two-parameter foundations in various different end conditions. The present analysis reflects the reliability, efficiency and simplicity of the proposed RDM in tackling boundary value problems. In fact, it is widely common that the critical load accompanied with the first buckling mode is the smallest critical load, and then it is the dominant factor in the static stability analysis. In contrast, the present analysis indicates that such a conclusion is correct only for the case of beams without foundations or in the case of a weak foundation relative to the beam. It is proved that critical loads accompanied with higher buckling modes may be smaller than those accompanied with the lower modes and then it may control the stability analysis. The same phenomenon exists for natural frequencies in the presence of an axial load. Several illustrations are introduced to highlight the effects of both the foundation stiffness and beam slenderness on the critical loads and natural frequencies.

3

Wpływ warstwy tworzywa EPY na dokładność posadowienia tocznej szyny prowadnicowej

Okulik T., Powałka B.

Archiwum Technologii Maszyn i Automatyzacji

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2009

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Vol. 29, nr 2

153-162

PL

W artykule zaprezentowano analizę dokładności posadowienia tocznej szyny prowadnicowej na warstwie tworzywa EPY. Porównano odchyłkę prostoliniowości dla dwóch przypadków montażu tych szyn. W pierwszym przypadku szyna była montowana na powierzchni szlifowanej według dotychczas stosowanej technologii, natomiast w drugim przypadku powierzchnia montażowa była obrobiona zgrubnie w operacji frezowania i posadowiona na cienkiej warstwie tworzywa EPY. Prostoliniowość powierzchni szyny badano za pomocą współrzędnościowej maszyny pomiarowej. Otrzymane wyniki porównano z analitycznymi modelami belek na podłożu sprężystym.

EN

Paper presents accuracy analysis of the guide rail mounted to a machine tool bed via EPY resin layer. Straightness deviation of the rail is compared for two analyzed cases, i.e. rail mounted using current technology and rail mounted on the milled surface via a thin layer of the EPY material. The rail was measured using CMM. Obtained results are compared to the solution of the beam on elastic foundation. The results show that the straightness error of the guide rail founded on the EPY is comparable with the guide mounted using current assembly technology.